With the game approaching a goalless draw, Issac Hayden's 94th minute header in front of the Gallowgate End secured a thrilling win for Steve Bruce's side.
Despite Chelsea's dominance in possession, the Blues were unable to find a breakthrough as United held firm, with Dúbravka recording a sixth clean sheet of the season in the process.
The goalkeeper told nufc.co.uk: "It was a perfect ending because they were a tough opponent today. They played really well with the ball and we were running without the ball a lot but we were very well organised and gave everything. It was a great effort and we were clinical.
"We played until the referee's whistle and you can see that from the games against Crystal Palace, Southampton and now against Chelsea. We hope that we can always make it difficult for teams to play against us, especially at St. James' Park.
"The fans are always behind us and it was amazing when we scored the goal. We appreciate that kind of support and it was an amazing atmosphere and feeling after the game.
"I'm also very pleased to keep the clean sheet. We were waiting a long time for it and I have to give credit to my team-mates because they were working really hard and helping me a lot so I'm delighted.
"I'm glad that we got payback over them after losing 1-0 in the last game. Now, it is 1-0 to us even if we did have two shots on target, with the first hitting the crossbar. Our strengths are team work and we worked really hard today."
The win elevates United into 12th place on 29 points, with the Magpies seven points above the relegation zone and five adrift of a European spot.
With attention quickly turning to Everton on Tuesday night, Dúbravka believes the impressive result against Frank Lampard's side will stand Newcastle in good stead for their trip to Merseyside in three days' time.
"Hopefully, this win can give us another good feeling," the 31-year-old added. "We knew that after three (league) defeats, it was difficult for us but as you could see, even against Chelsea you can take points.
"This game is definitely great for our confidence because you have so many games in such a short space of time. We have another game in three days so this gives us something special.
"I think it doesn't make a difference whether we win by scoring in the last minute or if we score in the 51st because, for me, the most important thing is winning and you could see that from the happy faces after the game."
